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NDA2021MathematicsApplication of DerivativesActual

What is the condition that f(x)=x^3+x^2+k x has no local extremum?

Options

  1. A4 k 1
  2. B3 k 1
  3. C3 k 1
  4. D3 k 1

Correct answer

B. 3 k 1

Step-by-step solution

aligned & f(x)=x^3+x^2+k x & f^ (x)=3 x^2+2 x+k aligned For no local extremum D 0 aligned & (2)^2-4(3)(k) 0 & 4 3 k 0 & 3 k 1 . aligned

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